State the meaning of simple harmonic motion.
A trolley is connected to two stretched springs, as shown in Fig. 4.1. The trolley is moved along the line joining the two springs and then released. At one point during the motion, a stopwatch is started. The variation with time $t$ of the trolley’s velocity $v$ is shown in Fig. 4.2. The motion of the trolley is simple harmonic.
State one time when the trolley passes through the equilibrium position and also state the next time that it passes through this position.
The amplitude of the trolley’s vibration is $3.2\,\text{cm}$. Find the trolley’s maximum speed $v_0$.
Find the trolley’s displacement for a speed of $\tfrac{1}{2}v_0$.
Use your answers in (b) to sketch, on the axes of Fig. 4.3, a graph showing how the velocity $v$ of the trolley varies with displacement $x$.